Mesh: the triangle primitive for three-cornered sweep regions

A cross-section region with three corners (a fillet's quarter disk, a
pocket corner cut off by a partition) was left to the free all-quad
mesher. It now gets midpoint subdivision's triangle primitive (Tam and
Armstrong 1991; Li, Armstrong, McKeag 1997): lines from a centre to a
node on each side split it into three mapped blocks, the interior then
smoothed and every quadrilateral checked (a fold falls back to free).
Interval assignment gains dominance constraints (a side shorter than
the other two together) so the split always exists.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/meshing/literature.md

@@ -991,7 +991,8 @@ record or the publisher; the others are cited by venue only.
   10(4):399–415, 2000). S. A. Mitchell. *Incremental interval assignment by integer linear algebra.*
   International Meshing Roundtable 2021 (Zenodo 5559025); extended in Computer-Aided Design 158:103485, 2023.
 - **Use.** Division counts of all curves together: side equalities of mapped faces and linking faces,
-  even (or multiple-of-four) loop sums, minimum loop sums. `hex::interval` uses incremental repair from the
+  even (or multiple-of-four) loop sums, minimum loop sums, and dominance (`Σ_A ≥ Σ_B + d`: a side of a
+  triangle primitive shorter than the other two together). `hex::interval` uses incremental repair from the
   rounded goals with increments only, chosen by squared relative error; it is bounded and reports an
   infeasible system instead of looping. Mitchell's integer-linear-algebra solver (Hermite normal form plus
   nullspace improvement) is the upgrade if the increment-only scheme proves too coarse.
@@ -1003,6 +1004,19 @@ record or the publisher; the others are cited by venue only.
   their reflex corners to the boundary, which decomposes rectilinear sections into rectangles (an explicit
   form of submapping's virtual decomposition), then mapped.
 
+**B8.6a Midpoint subdivision: Tam and Armstrong 1991; Li, Armstrong, McKeag 1997.** **Verdict: BUILD ON
+(triangle primitive).**
+- **Citations.** T. K. H. Tam, C. G. Armstrong. *2D finite element mesh generation by medial axis
+  subdivision.* Advances in Engineering Software 13(5–6):313–324, 1991. T. S. Li, C. G. Armstrong,
+  R. M. McKeag. *Quad mesh generation for k-sided faces and hex mesh generation for trivalent polyhedra.*
+  Finite Elements in Analysis and Design 26(4):279–301, 1997.
+- **Use.** A cross-section region with three corners (a fillet's quarter disk, a pocket corner cut off by
+  a partition) is split by lines from a centre to one node on each side into three mapped blocks
+  (`hex::region`, scheme `Triangle`): side `k` of `n_k` divisions splits into the counts of the two lines
+  that end beside it, so each line has `m_k = (n_{k+1} + n_{k+2} − n_k)/2` (an even loop, each side
+  shorter than the other two together). The centre is the mean of the split nodes; the interior is then
+  smoothed (`quad::smooth`) and every quadrilateral checked; a fold falls back to the free mesher.
+
 **B8.7 Gordon and Thiel 1982, trivariate transfinite interpolation.** **Verdict: BUILD ON (mapped blocks).**
 - **Citation.** W. J. Gordon, L. C. Thiel. *Transfinite mappings and their application to grid generation.*
   Applied Mathematics and Computation 10–11:171–233, 1982.